With a contact selected, click on the Send To arrow icon at the bottom of the window, and you can choose to send the card not just via email, but also via iMessage and AirDrop.

If you select the iMessage option, when the iMessage composition screen pops up, you can also use it as a quick shortcut to iMessaging the email address or phone number of your choosing: Just delete the card attachment inserted in the message body, and write whatever you'd like instead.